The L$acute{e}$vy copula can describe the dependence structure of a multidimensional L$acute{e}$vy process or a multivariate infinitely divisible random variable. Suppose the L$acute{e}$vy copula of a multidimensional L$acute{e}$vy process is known. We present the L$acute{e}$vy copula of the L$acute{e}$vy measure of the moving average driven by the multidimensional L$acute{e}$vy process. If there exist some special dependence structures among the components of the L$acute{e}$vy process, we give some dependence invariance properties after the transform of the moving average.